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Lie Groups Quantum Mathematics Seminar

Noncommutative Catalan numbers

Vladimir Retakh, Rutgers University

Location:  Hill 705
Date & time: Friday, 26 January 2018 at 12:00PM - 1:20PM

Abstract:We introduce and study noncommutative Catalan numbers C_ which belong to the free Laurent polynomial algebra in n generators. Our noncommutative numbers admit interesting (commutative and noncommutative) specializations, one of them related to Garsia-Haiman (q,t)-versions, another -- to solving noncommutative quadratic equations. We also establish total positivity of the corresponding (noncommutative) Hankel matrices H_ and introduce accompanying noncommutative binomial coefficients. 

Joint work with Berenstein (Oregon). See arXiv:1708.03316

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